Bane/PhysicsNotes
The following is a set of calculation notes of the physical properties of Bane by Anthony Hadley, approximating the correct values for its in-game description based on information taken from the Battlezone II website. The following are the calculations made to determine the correct values for bane.des, which previously used values copied directly from rend.des. Where possible I've taken variables from the BZII website; where this isn't possible I've derived estimates from said variables, and where that also isn't possible I've substituted values derived from appropriate comparison with Earth, Mire and/or Rend. GLOSSARY OF SYMBOLS USED: Ø - Diameter R - Radius P - Polar radius δ - Percentage difference |n| - Absolute value ~ - Approximation ξ - Random from set A - Surface gravity (acceleration due to gravity) D - Arbitrary scale factor E - Expected value (average of a possible range) <0, ..., n> - Average from set T - Temperature H - Solar irradiance r - Substituted radius d - Orbital radius h - Solar irradiance via substitution POLAR RADIUS P Here we find the percentage difference between Rend's equatorial and polar radii. Since Bane is in a less extreme situation than Rend, we're using those values as limits to add a random error to Bane's equatorial radius to stand in as a new polar radius. Ørend = 12000km game_worlds_rend.htm Rrend = Ørend/2 = 6000km Prend = 7654km rend.inf δrend = |21.670|% Øbane = 7400km game_worlds_bane.htm Rbane = Øbane/2 = 3700km δbane = ~δrend = |20|% Pbane = ξ((3700+20%), ..., (3700-20%)) = (3700+7.6486%) = 3983km SURFACE GRAVITY A Here we use both Earth and Rend's radii and surface gravities to calculate arbitrary scale factors. Averaging these scale factors produces a stand-in for Bane, which we can use to produce a stand-in for its surface gravity. Øearth = 12742km Aearth = 9.81ms^-2 Dearth = Øearth/Aearth = 1298.879 Ørend = 12000km Arend = 8.75ms^-2 rend.inf Drend = Ørend/A(rend) = 1371.429 Øbane = 7400km E(Dbane) = = <1298.879, 1371.429> = 1335.154 Abane = Øbane/E(Dbane) = 7400/1335.154 = 5.54ms^-2 BLACK-BODY TEMPERATURE T Having already been provided a temperature for Bane, we can simply convert it form one scale to another. T = -9C game_worlds_bane.htm T = 264.15K SOLAR IRRADIANCE H Here we begin with the standard formula for solar irradiance, substituting our sun in for the binary suns of the Core system and using scale factors derived from Mire and Rend's solar irradiance to draw the values back in line to the correct stars (essentially moving Bane to our solar system for the purposes of the calculation, then moving it back). Hbane = (Rsun^2/dbane^2)Hsun Hsun and Rsun are unknown and cannot be calculated due to Core system's binary nature. Substituting for Sol, using h for substituted irradiance: dbane = 2528.204e9 game_worlds_bane.htm hbane = (695700^2/2528.204e9^2)5.19e7 = 4.53 Comparison with Mire and Rend's actual values required to draw Bane's value back in line for correct system: dmire = 399.426e9 game_worlds_mire.htm hmire = (Rsun^2/dmire^2)Hsun = 181.41 Hmire = 1367.6 mire.inf Dmire = Hmire/hmire = 7.539 drend = 189.990e9 game_worlds_mire.htm hrend = (Rsun^2/drend^2)Hsun = 801.81 Hrend = 7533 rend.inf Drend = Hrend/hrend = 9.395 E(Dbane) = = <7.539, 9.395> = 8.467 Hbane = hbane*E(Dbane) = 4.53*8.467 = 38.36 MASS M Here we have rearranged the gravitational field equation to solve for mass, using values provided and calculated above. M = (AR^2)/G = ((5.54x3700)^2)/6.67408e-11 = 1.137e24kg ESCAPE VELOCITY V(esc) This is the standard calculation for escape valocity, so we can simply plug in above values. V(esc) = sqrt(2GM/R) = sqrt(2x6.67408e-11x1.137e24/3700) = 6.57km/s Category:Calculations